On a class of Finsler gradient Ricci solitons

Mo, Xiaohuan; Zhu, Hongmei; Zhu, Ling

doi:10.1090/proc/16240

On a class of Finsler gradient Ricci solitons
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by Xiaohuan Mo, Hongmei Zhu and Ling Zhu;

Proc. Amer. Math. Soc. 151 (2023), 1763-1773

DOI: https://doi.org/10.1090/proc/16240

Published electronically: January 13, 2023

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Abstract:

In this paper, we study a class of Finsler measure spaces whose weighted Ricci curvature satisfies ${\mathbf {Ric}}_{\infty }=cF^{2}$. This class contains all gradient Ricci solitons and Finsler Gaussian shrinking solitons. Thus Finsler measure spaces in this class are called Finsler gradient Ricci solitons. For a Randers measure space, we find sufficient and necessary conditions for this space to be a Finsler gradient Ricci soliton. In particular, we show that Randers-Finsler gradient Ricci solitons must have isotropic $S$-curvature. Finally, we give an equivalent condition for a Randers measure space to be a Finsler gradient Ricci soliton of constant $S$-curvature.

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